Papers

Bus holding can suppress bunching, but its stability and performance depend on the feedback structure and on how the bus sequence is bounded. This paper develops a common analytical framework for adaptive linear holding on finite open chains and loops and relates both to the bi-infinite system studied in the literature. Matrix and Fourier methods yield necessary and sufficient stability conditions for current- and leading-bus kernels on open chains and general cyclic kernels on loops, together with computable covariance bounds on open chains and exact variance formulas on loops. The analysis shows when periodic closure changes stability, when coefficient-sum stability tests in the literature are conservative, and why a stable open chain can still accumulate substantial variance before boundary effects arrive. For loops with same-lap feedback, modal analysis links control coefficients to fleet-wide schedule drift and to relative headway patterns, explaining the behavior of existing rules and yielding closed-form Pareto-optimal designs for schedule-holding and headway-holding tradeoffs. Cross-lap output corrections relate these designs to physical headway and holding performance. Numerical experiments show that the analytical design and a three-tap approximation, both obtained from closed-form coefficients and a one-dimensional search, outperform four established controls at the tested moderate and loose headway-variance budgets, with holding variances within 0.35% and 3.5% of the full cyclic numerical frontier across these budgets and other parameter variations. The framework thus provides a tractable design procedure and an explanation of how feedback structure and boundary conditions shape service reliability and holding effort.

We study interior Hessian estimates for $k$-convex solutions of Hessian quotient equations $\frac{\sigma_k(D^2u)}{\sigma_\ell(D^2u)}=1$ with $2\leq k\leq n$, $0 \leq \ell < k$, and $k-\ell \in\{1,2\}$. We first adopt the unified quantitative separation-propagation method of Li–Wu [LW26b] to derive a doubling inequality, and then use the compactness argument of Shankar–Yuan [SY25] to obtain the estimates. This approach also applies to a class of general Hessian equations.

Large-area molecular junctions combining photochromic and redox-active functionalities provide an attractive platform for controlling charge transport by light. In this work, we study Au/DAEVIO/Ti/Au molecular junctions incorporated with electro-grafted layers of diarylethene-viologen with thicknesses of 12-16 nm. In the initial OFF state, the junctions exhibit low current densities and strong rectification, with a rectification ratio of 300 at 1V. Temperature-dependent measurements reveal a thermally assisted contribution at higher temperatures and a much weaker temperature dependence below 160-180K, consistent with multistep charge transport through molecular and/or interfacial states rather than direct coherent tunneling across the entire molecular layer. Under continuous in situ 385 nm irradiation, the electrical response is strongly and asymmetrically modified. The current density at +1V increases by a factor of 200, while the negative-bias current is only weakly modified, reducing the rectification ratio from 300 to 2. Illumination also produces a nonzero short-circuit current density of + 0.006mA cm-2 and an open-circuit voltage of -0.45V. These results indicate that irradiation simultaneously modifies molecular charge transport and generates a measurable photoelectric response. This behavior is consistent with light-induced changes in electronic coupling associated with DAE photocyclization, combined with photoinduced charge generation and field-dependent charge separation involving the redox-active viologen units and asymmetric electrode interfaces.

We test the effective-gravity prediction of global thermodynamics using standard molecular dynamics of a two-dimensional Lennard-Jones fluid. Under weak heat conduction with the lower boundary hotter than the upper boundary, the transition between liquid below gas and liquid above gas shifts from zero to finite downward gravity. Using independently measured equilibrium saturation pressures, we calculate the shift predicted by global thermodynamics and find agreement with the observed transition shift. The transition occurs at zero effective gravity, where the hydrostatic pressure difference balances the saturation-pressure difference between the two boundaries. The hysteresis response under heat conduction also agrees with the equilibrium response when plotted against effective gravity. These results establish the predictive power of global thermodynamics for nonequilibrium structure formation.

This paper studies the complexity of model checking strategic abilities in multiagent systems under imperfect information, in particular systems represented succinctly. Such a representation can describe systems that are exponentially larger than their input and is particularly relevant to practical implementations of model checkers such as MCMAS. The logics we consider include epistemic strategy logic supporting partial binding $SLK_{P}$, and its syntactic fragments: epistemic strategy logic $SLK$ and variants of Alternating Time Temporal logics. We show that succinct model checking for $SLK_P$ and $SLK$ is $AEXP(poly)$-complete, while objective ATL and ATL$^{*}$ are $P^{NEXP}$-complete. The latter corrects a previous NEXP-completeness result for model checking succinct imperfect-information systems. Under subjective semantics, $P^{NEXP}$-completeness already holds for one-step Coalition Logic, and therefore also for ATL and ATL$^{*}$.

Benchmarks are essential for evaluating and improving large language models (LLMs). Yet many widely used benchmarks are redundant, making evaluation unnecessarily expensive. Benchmark compression lowers this cost by estimating full-benchmark scores and rankings from a partial evaluation. Research in this area has grown rapidly since 2024, but to our knowledge no survey has systematically organized its methods and findings. We review 119 papers to explain how methods choose what to evaluate, recover full-benchmark results, and verify their reliability. From this analysis, we develop a taxonomy covering compression within individual benchmarks, across benchmark suites, and during adaptive evaluation, together with work on redundancy and reliability. We compare their information needs, total costs, reliability checks, and limitations. Methods reduce evaluation costs by selecting representative subsets, using cheaper or reusable information, and testing adaptively, but risk poor coverage, inaccurate estimates, and sequential delays. The resulting taxonomy and practical guide help researchers choose, validate, and deploy methods for more efficient and reliable LLM evaluation.

Speech-to-speech translation should preserve not only what is said, but also who says it and how it is said. Existing end-to-end S2ST, speech MLLM, and cascade systems can preserve content or timbre, but often struggle to realize emotion, tone, rhythm, pauses, and pragmatic attitude in the target language. We propose PACT, a target-space pragmatic prompting framework for expressive and voice-preserving S2ST. PACT extracts source pragmatic cues, projects them into the target-language expression space, calibrates the projected representation to a realizable target subspace, and converts it into continuous prompts for a frozen speech generator. On bidirectional Spanish-English TOPI evaluation, PACT achieves the best overall performance among evaluated systems across content fidelity, voice preservation, and expression preservation metrics.

Let $\mathcal O$ be the Lubin–Tate deformation ring of a one-dimensional commutative formal group of finite height $n\geq1$ over a perfect field $k$ of characteristic $p$. We identify Rezk's Witt filtration $\{I_d\}$ with the divisibility filtration of integral trace pairings on subgroup algebras of fixed source lifts. This gives the geometric recursion \[ I_{d+1}=pI_d+J_{d,z}\qquad(d\geq0), \] where $J_{d,z}$ defines the targets of order-$p^d$ quotient isogenies from a $W(k)$-valued lift $z$ of the closed point. The corrected ideal is independent of $z$. We also compute the cokernel of the universal source trace pairing over $\mathcal O$: it is $\bigoplus_{j=1}^d(\mathcal O/p^j)^{r_j-r_{j-1}}$, where $r_j$ counts order-$p^j$ subgroups of $(\mathbf Q_p/\mathbf Z_p)^n$. The same duality extends the generic trace along two-step isogeny flags to an integral surjection, even when the flag-forgetting map is not flat. This computes composition in the subring of weighted trace operations. Applications include sharp projector denominators and congruence fibre products for full-torsion loci.

We report Zeus-256, a room-temperature nitrogen-vacancy (NV) diamond processor with 256 simultaneously active processor-level logical qubits arranged in a 16 x 16 array. Each logical qubit combines an NV electron-spin ensemble with nuclear-spin memory and ancillary resources. OpenQASM 2.0 circuits are transpiled into RFSoC-controlled microwave, radio-frequency, optical, timing, measurement and bus-configuration sequences. An optically programmable proprietary protein-chromophore layer with an internal metastable-triplet spin mediator provides a reconfigurable biomolecular quantum bus for local and long-range interactions. Benchmarks cover QFT, GHZ entanglement, Grover search, arithmetic, variational, neural-network, graph-state and Shor-family circuits. Factor recovery is reported for 11 integers of 8-84 bits, with 10 attempts per instance; the 84-bit endpoint uses 256 qubits and 40,250,342 reported gates, with a reported execution time of 551.694 ms. Bell-CHSH measurements yield S = 2.8008 +/- 0.0446. Three-qubit Grover search returns the marked state in 958 of 1,024 shots (93.55%), compared with an ideal reference of 94.53%. A separate 30,000-shot population-and-parity protocol yields fixed-phase GHZ+ fidelity of 99.8960%, an estimated standard error of 0.2885 percentage points and a conservative physical 95% interval of [98.2342%, 100%]. Timing metrics are partial and do not establish quantum advantage. Scaling to 9,984 processor-level logical qubits is an engineering target, distinct from the demonstrated register.

Transit compartment models are widely used in pharmacokinetics/pharmacodynamics to represent delayed biological processes such as absorption, maturation, cellular proliferation, and treatment-induced toxicity. This transit compartment formulation imposes an artificial relationship between the mean and variance of the delay distribution, as the number of transit compartment must be integer-valued number of transit compartments. Consequently, estimating the number of compartments from experimental data leads to mixed-integer optimization problems that artificially constrain model dynamics and bias parameter inference. However, these transit compartment models are mathematically equivalent to distributed delay differential equations with Erlang delay kernels. We leverage a hypoexponential generalization of these distributed delay differential equations that preserves the familiar ordinary differential equation structure while allowing the mean and variance of the delay distribution to be estimated directly as real-valued parameters. This approach does not increase the number of inferred parameters and can be immediately implemented as a straightforward modification of existing transit compartment models. We demonstrate the approach using models of viral eclipse phases, lymphocyte proliferation, and chemotherapy-induced neutropenia. Across these examples, the hypoexponential formulation provides comparable or improved fits relative to Erlang transit models and substantially reduces computational cost by avoiding grid search over compartment numbers. This framework provides a practical approach to estimate biologically meaningful delay distributions in quantitative systems pharmacology (QSP) models.

Given the growing global burden of liver tumors and diffuse liver diseases, non-contrast computed tomography (NCCT) is increasingly used for opportunistic screening because of its low cost and favorable safety profile. However, downstream tasks such as tumor detection and fine-grained disease diagnosis remain challenging due to NCCT's inherently low tissue contrast, lack of hemodynamic enhancement, and complex anatomical background. These limitations make subtle, heterogeneous, and multifocal hepatic lesions difficult to identify. Although large-scale self-supervised pretraining can learn robust representations from unlabeled NCCT scans, conventional voxel-wise reconstruction does not fully exploit the complementary information available in NCCT. Under weak NCCT contrast, low-level intensity patterns become less informative for pathology recognition, limiting the capture of lesion-specific discriminative features. In this paper, we propose the Liver Frequency-Spatial Unified Self-Supervised Pretraining (LiFUSE). The frequency branch applies random band-stop masking and spectrum reconstruction to encourage the model to capture subtle differences between lesions and surrounding tissues, while the spatial branch performs hybrid-granularity masked volumetric reconstruction to accommodate lesions of diverse sizes and morphologies. Finally, a cross-domain consistency scheme couples the spatial and frequency branches, yielding more discriminative representations for hepatic structures and lesions. Extensive experiments on three clinically relevant tasks across internal cohorts and a public target-domain transfer setting show that LiFUSE consistently outperforms strong baselines. These results suggest that unified frequency-spatial learning can improve liver disease analysis on NCCT, highlighting its potential for large-scale screening.

We propose a model for the one-dimensional isothermal gas flow through a valve in a pipe. The valve aims at keeping the outgoing flow in an assigned interval; moreover, its opening and closing depend on a further parameter. The model is realized by a system of two conservation laws with suitable conditions coupling the ingoing and the outgoing flow. We study the corresponding Riemann problem, where non-classical shocks show up. Although simple, the model allows to study two key oscillatory behaviors of the flow, which are due, respectively, to the chattering of the valve, especially seen in the numerical simulations, and to the stabilizing hysteresis induced by the valve operation. We characterize the states leading to chattering and show how they depend on the parameters of the model. Through several numerical simulations, we study the interplay between the two above phenomena.

We study a massive scalar field in flat spacetime written in a time-dependent accelerated frame whose fixed-coordinate observers have maximal proper acceleration at $t=0$ and become asymptotically inertial without forming a horizon. The Klein-Gordon equation separates into a modified Mathieu equation in time and a confining Schrödinger problem in space with a discrete spectrum. We impose an adiabatic vacuum at the instant of maximal acceleration and compute the particle number in the inertial future. For the zeroth-order adiabatic state it falls as the inverse eighth power of the initial mode frequency, and raising the adiabatic order cancels successive terms of the endpoint expansion, in analogy with the switching transients of finite-time detectors. Analytic continuation of the spatial eigenfunctions gives the out modes in closed form and an exact expression for the particle number, which is entirely the mismatch at $t=0$ between the initial state and the out vacuum. The spectrum is algebraic rather than Planckian.

Multi-agent debate (MAD) aims to improve large language model reasoning by exposing agents to alternative solutions and enabling iterative revision. However, standard broadcast-style MAD makes peer answers visible without requiring agents to engage with a particular peer claim. As a result, reliable reasoning may be suppressed by conflicting or majority responses, limiting achievable performance, while erroneous reasoning may persist and degrade final predictions without actionable feedback. We propose TrueMAD, a backbone-agnostic test-time plug-in that introduces one-to-one, free-form peer advice between answer broadcasting and self-revision. Each source agent responds to a target's current reasoning through support, rebuttal, refinement, or further questions, while the target retains control over how to revise. The same mechanism can augment standard MAD and its improved variants without parameter updates. Across AIME, GPQA-Diamond, and TruthfulQA with Qwen3-30B-A3B, TrueMAD improves agent-level and strict-majority accuracy over MAD by 3.62 and 3.52 percentage points on average, while TrueDMAD improves DMAD by 4.72 and 4.06 points, respectively. Analyses at the utterance, agent-transition, and group levels further show more peer-specific deliberation, more correction-oriented revisions, and more favorable consensus dynamics.

We introduce river ribbon tableaux, where a river of non-trivial ribbons is placed between two banks of single boxes. Compared to other ribbon peelings, this reduces the geometric differences across diagrams of different shapes, and the maximal number of ribbon configurations. This allows us to prove a uniform character bound for symmetric groups which, specialized to balanced diagrams, proves the conjecture of Moore and Russell. As an application, we prove a conjecture of Dousse and Féray on the number of standard tableaux of skew shapes.

Vision-language models (VLMs) have been widely adopted for document parsing and optical character recognition (OCR), as they can accurately extract page-level elements. However, downstream applications such as retrieval-augmented generation (RAG) also require coherent document-level structure. Although these models indicate heading levels using different numbers of preceding “\#” symbols, page-by-page prediction often lacks document-level consistency. In practice, input-resolution and context-length constraints make it infeasible for a VLM to jointly process all page images in documents containing tens or hundreds of pages. To address this limitation, we propose a VLM-based framework that incrementally reconstructs heading hierarchies with a level-wise multimodal memory. The memory retains a compact subset of all previously processed pages, selected by anchors. Our framework supports flexible anchor selection, and in this work we select the most recent node at each level, allowing the VLM to observe the visual, textual, and layout patterns of headings at every level. For comprehensive evaluation, we also introduce the Complex and Long Document Heading Hierarchy Reconstruction Benchmark (CLDoc-HHRBench), comprising 250 documents and 11,212 pages with expert-verified annotations. Experiments on CLDoc-HHRBench and three existing benchmarks demonstrate the effectiveness of our method.

We present a fully autonomous model of a mechanical Maxwell demon engine that converts heat absorbed by a qubit into population inversion in an attached quantum battery. A damped mechanical oscillator acts as a pointer that incorporates the essential demon function of information acquisition about the qubit state and subsequent feedback into the system dynamics, replacing external measurements and control operations. This is achieved by means of a Holstein-type Hamiltonian, which makes the pointer's equilibrium position depend on the qubit state and thereby induces a state-dependent resonance shift. The mechanism enables a selective energy transfer to an attached spin system that acts as the quantum battery. We derive both local and global Lindblad master equations for the coupled system and identify the parameter regimes in which the engine operates efficiently. The figure of merit is the resulting steady-state population inversion of the battery, quantified in terms of ergotropy. Based on these results, we discuss the necessary conditions for practical implementations of the demon engine on realistic experimental platforms.

Quantum devices can lose the resource needed for a specified function without entering a fixed failure subspace. We propose a resource-based reliability framework for this situation, quantifying the remaining task-relevant resource relative to a stated ideal capacity. The resource measure is selected through its operational connection to the task and the allowed operations. We develop this approach for a trusted quantum random-number generator and a calibrated two-port interferometer. Relative-entropy coherence determines the optimal asymptotic yield of standard coherent qubits under incoherent operations for the former, while logarithmic $l_1$ coherence quantifies the fringe resource of the latter and determines its calibrated correct-port probability. An exactly solvable multi-spin spin-boson model illustrates how environmental records affect these resources at the same isolated-spin dephasing strength. Collective noise preserves coherence within magnetization sectors for product inputs, but enhances the decay of Greenberger-Horne-Zeilinger branch coherence. Finite-record simulations connect the resource definitions to measurement counts and show that increasing the sample size reduces statistical fluctuations without eliminating bias from an incorrect many-spin noise model. The resulting framework provides a task-specific route to reliability assessment when a fixed failure projector is insufficient, while keeping retained resource capacity distinct from a classical survival probability.

Let $P_{n,k}$ count permutations of $[n]=\{1,\ldots,n\}$ whose longest increasing subsequence has length $k$. Chen conjectured that $(P_{n,k})_{k=1}^n$ is log-concave for every positive integer $n$. In this paper, we prove that Chen's conjecture is true when $n\ge 10^{10^{65}}$. The proof combines Gessel's determinantal formula with quantitative coefficient extraction, Tracy–Widom density estimates, and exact inequalities for the extreme lengths.

The LZ collaboration has recently reported a single nuclear-recoil event at $E_R=248\pm23_\text{stat}\pm23_\text{sys}$ keV, observed in a 2.84 tonne-year exposure with a local significance of $3.4\sigma$, pointing towards an inelastic dark matter (DM) interpretation. We explain this event within a gauged $U(1)_X$ hidden-sector model, spontaneously broken by a singlet scalar whose vacuum expectation value (VEV) gives rise to: (i) gauge boson mass, (ii) a small Majorana mass for the vector-like singlet fermion, the DM candidate, charged under the new symmetry, which splits the fermion into two pseudo-Dirac states (mass splitting proportional to the scalar VEV) thus resulting in a purely off-diagonal vector current, (iii) the frequency and the amplitude of the GW signal arising from the hidden sector symmetry breaking via first-order phase transition (FOPT). The symmetry-breaking scale thus provides a multi-messenger probe connecting terrestrial direct-detection kinematics at the LZ and early-universe FOPT thermodynamics while obtaining thermal DM relic abundance. We delineate the viable parameter space compatible with the LZ event, correct relic density, and detectable GW signals in the low frequency regimes at future interferometers like $\mu {\rm ARES}$ and THEIA while satisfying existing cosmological, astrophysical, and terrestrial bounds.

System One models answer typed questions in a single forward pass and promise the same answer for the same input. For choice questions, this promise fails: the answer depends on the order of the options, increasingly so as they grow in number, and averaging over their cyclic shifts reduces this dependence without removing it. Scoring each option alone, which the order cannot affect, shows that the order changes the answer mostly when the model is unsure among its top few options, even though the listwise answer looks confident. We therefore propose $\textbf{Runoff}$, which considers, then chooses: it scores each option alone to keep a few candidates, then compares them in listings where each candidate takes every position. It needs no training and can run in two forward passes, and its answer does not depend on the option order by construction. On two open models and five datasets, it changes no answer under shuffling, against 9.3% for cyclic averaging, and with 20 options it is about as accurate and three to four times faster. Wrapped around eight System One models, it removes the order dependence of the five benchmarks, while cyclic averaging changes up to 15.4%.

In many applications, covariates are naturally organized into groups, yet conventional group-selection methods often retain all variables within selected groups, failing to achieve within-group sparsity. To address this limitation, we propose an adaptive two-stage sparse-group selection procedure for high-dimensional quantile regression. The proposed method integrates convolution-smoothed quantile loss with $\ell_{2,0}$ and $\ell_0$ penalties to identify important groups and relevant variables within them, achieving sparsity at both levels. We establish theoretical guarantees for sure screening and exact support recovery at both stages, as well as consistent model-size selection using information criteria, with explicit bounds on failure probabilities. The proposed procedure is computationally efficient by restricting optimization to selected groups and active variables. Simulation studies and a breast cancer gene-expression analysis demonstrate its competitive performance in variable selection, estimation accuracy, and computational efficiency, while identifying biologically relevant genes and delivering accurate quantile predictions.

Smoothed decentralized Bregman proximal-gradient (SDBPG) methods combine relative-smoothness geometry with edge-dual consensus. We extend SDBPG to node-specific convex nonsmooth regularizers and unbiased stochastic local gradients while retaining its Bregman primal-dual smoothing mechanism. The analysis isolates temporal subgradient motion and aggregation mismatch as two defect sequences. For trajectories in a forward-invariant compact subset of the kernel domain and admissible parameters, finite accumulated defects yield an $O(T^{-1})$ bound on the squared best-iterate proximal residual over $T$ iterations. The stochastic bound separates accumulated oracle variance from expected defects and attains the same order when the variance bounds and expected defects are summable. Common active-structure identification, together with local subgradient conditions, gives sufficient finite-defect conditions for $\ell_1$ and group $\ell_{2,1}$ regularization. Experiments with common regularizers and heterogeneous sensing operators relate defect decay to observed support stabilization and compare reconstruction and communication with decentralized proximal and gradient-tracking methods. A separate phase-retrieval study evaluates the effect of a quartic Bregman kernel. Code and experiment scripts are available at https://github.com/shengze-xu/composite-stochastic-sdbpg .

While AI agents are useful for many tasks, they regularly misbehave in destructive ways, such as deleting important data. While prior work has focused on preventing such misbehavior, we consider how to recover after an agent misbehaves. We propose verifiable agent insurance (VAI), a framework for agent providers to commit financially to promises, a list of programmatically-specified policies that an agent is meant to follow. These promises are embedded in a smart contract on an immutable ledger (e.g., a blockchain) to prevent tampering, along with a monetary escrow. A user who detects a violation of committed promises can prompt a verifier to review agent execution traces, which are logged through the agent harness's shared tool-execution path, without instrumenting each tool separately. Upon verification of the violation, the agent provider's escrow funds are paid to the reporting user. We instantiate VAI as an end-to-end implementation on an Ethereum layer-2 network, and evaluate its coverage on three prominent agent benchmarks, two of which we re-annotated to obtain task-level policy-compliance labels. Currently, many agents do not emit user authorizations and security-relevant information as explicit, structured data objects – rather, they embed the data needed to verify policy violations in natural language exchanges. Even so, VAI manages to detect violations in 42.2% of runs containing violations across three benchmarks. By augmenting agents to explicitly emit such objects, violation detection rises to 83.0% of traces. Our findings suggest that for improved auditability, agents should be co-designed with their security policies to emit explicit, structured records of user authorization and security-relevant actions.

Deep reinforcement learning agents in partially observable competitive games must act on beliefs about an unseen opponent's intent. We study a spatial opponent model: a transformer trained with hindsight-relabelled opponent goals that outputs a subgoal heatmap from the opponent's observed trajectory, fused early into a dueling double DQN. In symmetric constant-sum foraging games with partial observability, the module stabilises training. Plain TD(0) DQN suffers degenerate seeds in three of four one-step configurations, whereas the opponent-model agent never collapses and, wherever training succeeds, recovers the majority of the symmetric game value. Transfers zero-shot to a foraging opponent unseen by the learner, with a positive goal advantage over the baseline, and loses this edge exactly where an information argument predicts: against a full-information tracking adversary whose intent is the learner itself, and on resource-dense maps where both agents saturate. A blindfold ablation, zeroing the heatmap at deployment, decomposes the advantage into two mechanisms: training-time stabilisation, which dominates where the credit assignment is hard and survives blinding on the dense map, and deployment-time inference, whose reliance shrinks as fog thins on the sparse map. We conclude that opponent-goal inference is a stability-and-transfer mechanism whose value is governed by measurable boundary conditions: visibility (fog thickness), opponent intent, and resource density.

We give a counterexample to the implication from generic local to generic global identifiability for linear networks with a fixed topology, independently unknown edge coefficients, and selected excited and measured nodes. A six-node network with nine unknown coefficients has exactly two compatible parameter vectors generically. Adding six excited and measured nodes preserves this ambiguity while making the added coefficients directly recoverable. The resulting twelve-node structure has forty-two independent unknown coefficients and zero diagonal. For every positive bound on the largest eigenvalue magnitude, a nonempty open set of parameters has two distinct compatible networks satisfying that bound. This holds for both real and complex coefficients. Other open regions have exactly one admissible solution. The proof uses a rational transformation exchanging the two solutions and a common limiting matrix whose fourth power vanishes. Exact rational-number certificates verify an explicit pair. The construction also extends algebraically when the unknown coordinates are whole rational transfer functions. Genericity in prescribed numerator and denominator coefficient families, and the requirement that every transfer function vanish at infinite frequency, remain separate questions.

Domain-specific curvature is an appealing idea for domain generalization (DG), but curvature learning can denote substantially different computations. This paper evaluates one deliberately narrow implementation: the code calls it HyperDG, but it rescales Euclidean encoder features during training by learned positive scalars and uses an ordinary linear classifier on unscaled Euclidean features at inference. It does not implement a Lorentz or Poincaré representation, geodesic prediction, or a Sharpness-Aware Minimization inner loop. We audit the executed objective and evaluate six conditions on PACS, VLCS, Office Home, and TerraIncognita. The completed design contains 384 runs: six conditions, four held-out targets, and four run seeds per dataset. Checkpoints are selected using only the three source-validation environments. Inference first averages paired seed differences within each held-out target; targets, rather than 16 seed-by-target observations, are the per-dataset clusters. The full implementation's equal-dataset macro point estimate is 1.61 percentage points below native DomainBed ERM (95% clustered CI [-3.17, -0.04]). All four dataset point estimates favor ERM, but an exact four-dataset sign-flip test gives p = .125 and Holm-adjusted p = .250; we therefore claim no adjusted evidence of a difference. The cleaner domain-specificity contrast, separate learned source scales without their variance penalty versus one shared learned source scale, is -0.13 pp (95% CI [-0.53, 0.27]). Its 90% CI lies within a revision-stage $\pm 1$ pp smallest effect of practical interest (TOST p = .003), supporting equivalence only for the source-selected suite macro, not every dataset, target, or final-step endpoint. The study thus supplies a bounded negative result for this scalar training package; it does not test or refute genuine hyperbolic representation learning.

Let $f$ be a monic polynomial of degree $n$ with integer coefficients. We use Fourier analysis to prove a new upper bound on the number of $n\times n$ matrices with characteristic polynomial $f$ and integer entries in $[-T,T]$, as $T\to \infty$. The implied constant in our bound only depends on $n$ and is otherwise uniform in $f$. Our bound improves on recent work of Habegger, Ostafe and Shparlinski for $n\geq 4$.

Quantum computers are approaching the early fault-tolerant regime. Verifying the next generation of quantum hardware requires joint emulation of the quantum processor, hardware noise, and classical control and decoding logic. We introduce the Programmable Pauli Virtual Machine (PPVM), an open-source framework for digital twins of quantum processors. PPVM unifies Pauli propagation and generalized tableau simulation under a common abstraction within a single virtual machine. Its bytecode supports arbitrary classical control flow, with measurement-conditioned feed-forward available in the generalized tableau backend. For neutral-atom hardware, we derive independent and correlated atom-loss channels and integrate them into both backends. We demonstrate loss-aware magic state distillation on over a thousand physical qubits and integration with classical decoding through Bloqade QEC Studio.

We uncover an intrinsic gyrotropic spin current (IGSC) driven solely by an oscillating magnetic field, arising from the spin version of Zeeman quantum geometry. Using the density matrix formalism, we derive the IGSC in the low-frequency clean limit, in terms of the Zeeman spin quantum metric and the Zeeman spin Berry curvature. The effect is studied in a minimal Rashba-Dresselhaus model that also supports intrinsic gyrotropic charge currents from the Zeeman Berry curvature. The spin and charge currents exhibit a $\pi/2$ phase shift and are found to be perpendicular to each other for certain parameter ranges. This not only enables spin current detection but also opens pure spin current channels for energy-efficient spintronics. We further observe that these currents switch directions between longitudinal and transverse relative to the applied field, depending on the relative strength of Rashba and Dresselhaus interactions.